This paper introduces an innovative data-driven approach to uncertainty quantification (UQ) in complex engineering designs based on polynomial chaos expansion (PCE) and least-square support-vector machine (LSSVM). While PCE is a prevalent UQ method, its reliance on a predefined model form poses limitations in the model complexity, training accuracy, and efficiency in high-dimensional settings. To overcome this, we propose a nonparametric reformulation that draws equivalence with the kernel-based LSSVM. Leveraging special implicit kernels based on Hermite or Legendre polynomials, our method achieves accurate predictions with reduced training data. The model is trained through the dual space LSSVM formulation, thereby exploiting the so-called “kernel trick”, while PCE coefficients up to an arbitrary order are efficiently obtained post-training. Validation encompasses a diverse range of scenarios, including standard benchmarks and real-life applications in electrical engineering involving up to 26 independent random input parameters. The proposed “PCE-LSSVM” method exhibits superior performance over traditional PCE implementations. It achieves up to 7 times smaller root-mean-square error and up to 10 times lower dispersion across various training datasets, showcasing superior performance even with a significantly reduced number of training samples. Notably, this approach is 2 to 50 times more efficient compared to alternative approaches such as ordinary least square regression or Gaussian quadratures. Overall, PCE-LSSVM emerges as a powerful and efficient tool for accurate UQ in complex engineering systems.

This article introduces a probabilistic machine learning framework for the uncertainty quantification (UQ) of electronic circuits based on the Gaussian process regression (GPR). As opposed to classical surrogate modeling techniques, GPR inherently provides information on the model uncertainty. The main contribution of this work is twofold. First, it describes how, in a UQ scenario, the model uncertainty can be combined with the uncertainty of the input design parameters to provide confidence bounds for the statistical estimates of the system outputs, such as moments and probability distributions. These confidence bounds allow assessing the accuracy of the predicted statistics. Second, in order to deal with dynamic multioutput systems, principal component analysis (PCA) is effectively employed to compress the time-dependent output variables into a smaller set of components, for which the training of individual GPR models becomes feasible. The uncertainty on the principal components is then propagated back to the original output variables. Several application examples, ranging from a trivial RLC circuit to real-life designs, are used to illustrate and validate the advocated approach.

This paper focuses on a preliminary study on the spectral analysis of linear time-varying circuits for the prediction of their stead-state and transient behavior. The proposed approach is based on the integral representation of the circuit equations in either the Fourier or Laplace domains. It provides the readers with an elegant and robust tool for the frequency-domain simulation of this class of circuits, enabling the direct inclusion of frequency-dependent elements. The feasibility and strength of the method are demonstrated on two illustrative examples consisting of a periodically linear time-varying parallel resonators and a simple time-varying circuit.